There are several Campaigns in the Campaign Book Volume 1, and each one is going to be a bit of a different answer...so before anyone can help you figure out which side to take, it might be good to tell us which Campaign you plan on playing!

Well if you don want to change the course of history, play as Axis in Normandy, French in Fall Gelb and as Soviet in Barbarossa Campaign. But if you want to have bigger chance to win, play quite opposite sides.

I would recommend playing as axis. On average they are grossly outnumbered in the game, have smaller hands and several cards give them a disadvantage, most clearly in the air power card. Most expansions give extra positive rules allied nations, while Germany leaps behind. The exceptions are soviet union with commissar, and tiger tanks (debatable though).

But that's not the point of the campaigns. The secondary objectives allow for catch up in total point numbers, so while individual battles might not be entirely balanced, the campaign as a whole is intended to be more so.

Also, like tinsoldier, I suggest playing both sides. The games take longer to set up than to play. So, when I play a campaign, I play the scenario at least 2 times, sometimes 4 (since chances are I won't be setting it up again soon).